Download Prove Triangles are Congruent

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Prove Triangles are Congruent by - SSS, SAS, HL, ASA, AAS
Vocabulary
Definition
Example
̅̅̅̅ ≅ _____,
If Side AB
SIDE-SIDE-SIDE
(SSS)
CONGRUENCE
POSTULATE
If three sides of one triangle are congruent to
three sides of a second triangle, then the two
triangles are congruent.
̅̅̅̅ ≅ _____, and
Side BC
̅̅̅̅ ≅ _____,
Side CA
then ΔABC ≅ Δ_______.
LEG of a RIGHT
TRIANGLE
In a right triangle, a side adjacent to the right
angle is called a leg.
HYPOTENUSE
In a right triangle, the side opposite the right
angle is called the hypotenuse.
SIDE-ANGLE-SIDE
(SAS)
CONGRUENCE
POSTULATE
If two sides and the included angle of one
triangle are congruent to two sides and the
included angle of a second triangle, then the two
triangles are congruent.
̅̅̅ ≅ _____,
If Side ̅RS
*INCLUDED ANGLE- In a triangle, the angle formed by
then ΔRST ≅ Δ_______.
two sides is the included angle for those two sides.
Angle ‹R ≅ _____, and
Side ̅̅̅̅
RT ≅ _____,
HYPOTENUSE-LEG
(HL) CONGRUENCE
THEOREM
ANGLE-SIDEANGLE (ASA)
CONGRUENCE
POSTULATE
If the hypotenuse and a leg of a right triangle are
congruent to the hypotenuse and a leg of a second
triangle, then the two triangles are congruent.
If two angles and the included side of one
triangle are congruent to two angles and the
included side of a second triangle, then the two
triangles are congruent.
*INCLUDED SIDE- Suppose you were given the measure of
If Angle ‹A ≅ _____,
Side ̅̅̅̅
AC ≅ _____, and
Angle ‹C ≅ _____,
then ΔABC ≅ Δ_______.
two angles in a triangle. This refers to the side between
them.
If Angle ‹A ≅ _____,
ANGLE-ANGLESIDE (AAS)
CONGRUENCE
THEOREM
If two angles and a non-included side of one
triangle are congruent to two angles and the
corresponding non-included side of a second
triangle then the two triangles are congruent.
Angle ‹C ≅ _____, and
̅̅̅̅ ≅ _____,
Side BC
then ΔABC ≅ Δ______.